The objective of this research is to form high-resolution and quantitative ultrasonic images of the breast using significant advances in adaptive aberration correction and in inverse scattering theory in combination with an innovative ring transducer system that has programmable transmit waveforms. High-resolution b-scan images will be formed and evaluated for their utility in the diagnosis of breast cancer. Image formation will employ new adaptive focussing techniques. In one technique, transmit signals are synthesized from scattered signals using backpropagation followed by time-shift estimation and compensation. The synthesized waveforms are predistorted for the particular breast tissue path so that propagation to the focal zone reverses the distortion and yields an undistorted focus for point and contrast resolution limited only by aperture size and pulse length rather than by aberration. Focussing in reception employs backpropagation followed by time-shift compensation. In another technique, ultrasonic wavefronts are processed in one of four domains: space, spatial frequency, time, and temporal frequency. Forward and backward propagation over a selectable distance is used to change the temporal and spatial characteristics as well as the temporal frequency and spatial frequency characteristics of the wavefront. Without the need for a point source, both techniques correct for the effects of inhomogeneities throughout the propagation path between the transducer and the region being imaged. Quantitative images of breast tissue intrinsic parameters such as sound speed, compressibility, and density will be formed using significant advances in the theory of image reconstruction. The advances yield optimal insonifications, estimation of scatterer properties from analysis of operators derived from measured scattering data, and new image reconstruction methods. Data for the construction of both high-resolution b-scan images and quantitative images will be obtained from various phantoms and numerous breast specimens. The resulting images will be compared with observed morphology of scattering objects and the imaging techniques will be critically evaluated for their utility in breast cancer detection, diagnosis, and monitoring for recurrence. Criteria for this evaluation include point and contrast resolution, computational simplicity, and the ability of quantitative images to show new information that is concealed in b-scans by compensatory changes in tissue parameters.